File: The-Lognormal-Distribution.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (109 lines) | stat: -rw-r--r-- 5,911 bytes parent folder | download
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".

(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: The Lognormal Distribution</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: The Lognormal Distribution">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: The Lognormal Distribution">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Random-Number-Distributions.html#Random-Number-Distributions" rel="up" title="Random Number Distributions">
<link href="The-Chi_002dsquared-Distribution.html#The-Chi_002dsquared-Distribution" rel="next" title="The Chi-squared Distribution">
<link href="The-Flat-_0028Uniform_0029-Distribution.html#The-Flat-_0028Uniform_0029-Distribution" rel="previous" title="The Flat (Uniform) Distribution">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="The-Lognormal-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Chi_002dsquared-Distribution.html#The-Chi_002dsquared-Distribution" accesskey="n" rel="next">The Chi-squared Distribution</a>, Previous: <a href="The-Flat-_0028Uniform_0029-Distribution.html#The-Flat-_0028Uniform_0029-Distribution" accesskey="p" rel="previous">The Flat (Uniform) Distribution</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="The-Lognormal-Distribution-1"></a>
<h3 class="section">20.17 The Lognormal Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005flognormal"></a>Function: <em>double</em> <strong>gsl_ran_lognormal</strong> <em>(const gsl_rng * <var>r</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dd><a name="index-Lognormal-distribution"></a>
<p>This function returns a random variate from the lognormal
distribution.  The distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} } \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx
</pre></div>

<p>for <em>x &gt; 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005flognormal_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_lognormal_pdf</strong> <em>(double <var>x</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a lognormal distribution with parameters <var>zeta</var> and <var>sigma</var>,
using the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005flognormal_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_lognormal_P</strong> <em>(double <var>x</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005flognormal_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_lognormal_Q</strong> <em>(double <var>x</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005flognormal_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_lognormal_Pinv</strong> <em>(double <var>P</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005flognormal_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_lognormal_Qinv</strong> <em>(double <var>Q</var>, double <var>zeta</var>, double <var>sigma</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(x)</em>, <em>Q(x)</em> and their inverses for the lognormal
distribution with parameters <var>zeta</var> and <var>sigma</var>.
</p></dd></dl>





</body>
</html>